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Doping effects on the stacking fault energies of the γ' phase in Ni-based superalloys

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Chinese Physics B 2020年第2期29卷 390-395页

作者： Weijie Li Chongyu Wang Department of Physics Tsinghua UniversityBeijing 100084China Institute of Applied Physics and Computational Mathematics Beijing 100088China

The doping effects on the stacking fault energies(SFEs),including the superlattice intrinsic stacking fault and superlattice extrinsic stacking fault,were studied by first principles calculation of the/phase in the Ni-based *** formation energy results show that the main alloying elements in Ni-based superalloys,such as Re,Cr,Mo,Ta,and W,prefer to occupy the Al-site in Ni3 AI,Co shows a weak tendency to occupy the Ni-site,and Ru shows a weak tendency to occupy the *** SFE results show that Co and Ru could decrease the SFEs when added to fault planes,while other main elements increase *** double-packed superlattice intrinsic stacking fault energies are lower than superlattice extrinsic stacking fault energies when elements(except Co) occupy an ***,the SFEs show a symmetrical distribution with the location of the elements in the ternary model.A detailed electronic structure analysis of the Ru effects shows that SFEs correlated with not only the symmetry reduction of the charge accumulation but also the changes in structural energy.

关键词： stacking fault energy site preference Ni-based superalloys electronic structure

Conformal prediction after efficiency-oriented model selection

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arXiv 2024年

作者： Liang, Ruiting Zhu, Wanrong Barber, Rina Foygel Committee on Computational and Applied Mathematics University of Chicago United States Department of Statistics University of California Irvine United States Department of Statistics University of Chicago United States

Given a family of pretrained models and a hold-out set, how can we construct a valid conformal prediction set while selecting a model that minimizes the width of the set? If we use the same hold-out data set both to select a model (the model that yields the smallest conformal prediction sets) and then to construct a conformal prediction set based on that selected model, we suffer a loss of coverage due to selection bias. Alternatively, we could further splitting the data to perform selection and calibration separately, but this comes at a steep cost if the size of the dataset is limited. In this paper, we address the challenge of constructing a valid prediction set after efficiency-oriented model selection. Our novel methods can be implemented efficiently and admit finite-sample validity guarantees without invoking additional sample-splitting. We show that our methods yield prediction sets with asymptotically optimal size under certain notion of continuity for the model class. The improved efficiency of the prediction sets constructed by our methods are further demonstrated through applications to synthetic datasets in various settings and a real data example. Copyright © 2024, The Authors. All rights reserved.

关键词： Prediction models

HEAT AND MARTIN KERNEL ESTIMATES FOR SCHRÖDINGER OPERATORS WITH CRITICAL HARDY POTENTIALS

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arXiv 2022年

作者： Barbatis, Gerassimos Gkikas, Konstantinos T. Tertikas, Achilles Department of Mathematics National and Kapodistrian University of Athens Athens15784 Greece Department of Mathematics & Applied Mathematics University of Crete Heraklion70013 Greece Institute of Applied and Computational Mathematics FORTH Heraklion71110 Greece

Let Ω be a bounded domain in RN with C2 boundary and let K ⊂ ∂Ω be either a C2 submanifold of the boundary of codimension k 2/4. We establish parabolic boundary Harnack inequalities as well as related two-sided heat kernel and Green function estimates. We construct the associated Martin kernel and prove existence and uniqueness for the corresponding boundary value problem with data given by measures. Next we apply the results to the study of Lµu+g(u) = 0 and establish existence and uniqueness under suitable assumptions on the function g. To prove our results we introduce among other things a suitable notion of boundary trace. This trace is different from the one used by Marcus and Nguyen [MN1] thus allowing us to cover the whole range µ ≤ k2/*** Codes Primary 35K08, 35J25, 35J75, 35J08. Secondary 46E35, 31C35 © 2022, CC BY.

关键词： Boundary value problems

Nonparametric Density Estimation via Variance-Reduced Sketching

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arXiv 2024年

作者： Peng, Yifan Khoo, Yuehaw Wang, Daren Committee on Computational and Applied Mathematics University of Chicago United States Department of Statistics University of Chicago United States Department of Statistics University of Notre Dame United States

Nonparametric density models are of great interest in various scientific and engineering disciplines. Classical density kernel methods, while numerically robust and statistically sound in low-dimensional settings, become inadequate even in moderate higher-dimensional settings due to the curse of dimensionality. In this paper, we introduce a new framework called Variance-Reduced Sketching (VRS), specifically designed to estimate multivariable density functions with a reduced curse of dimensionality. Our framework conceptualizes multivariable functions as infinite-size matrices, and facilitates a new sketching technique motivated by numerical linear algebra literature to reduce the variance in density estimation problems. We demonstrate the robust numerical performance of VRS through a series of simulated experiments and real-world data applications. Notably, VRS shows remarkable improvement over existing neural network estimators and classical kernel methods in numerous density models. Additionally, we offer theoretical justifications for VRS to support its ability to deliver nonparametric density estimation with a reduced curse of dimensionality. Copyright © 2024, The Authors. All rights reserved.

关键词： Matrix algebra

Stability and related zero viscosity limit of steady plane Poiseuille-Couette flows with no-slip boundary condtion

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arXiv 2022年

作者： Jiang, Song Zhou, Chunhui Department of Mathematics Southeast University Nanjing210096 China Institute of Applied Physics and Computational Mathematics Beijing China

We prove the existence and stability of smooth solutions to the steady Navier-Stokes equations near plane Poiseuille-Couette flow. Consequently, we also provide the zero viscosity limit of the 2D steady Navier-Stokes equations to the steady Euler equations. First, in the absence of any external force, we prove that there exist smooth solutions to the steady Navier-Stokes equations which are stable under infinitesimal perturbations of plane Poiseuille-Couette flow. In particular, if the basic flow is the Couette flow, then we can prove that the flow is stable for any finite perturbation o(1). Moreover, we also show that for any smooth shear flow satisfying (1.27), if we put a proper external force to control the flow, then we can also obtain a smooth solution of the steady Navier-Stokes equations which is stable for infinitesimal perturbation of the external force. Finally, based on the same linear estimates, we establish the zero viscosity limit of all the solutions obtained above to the solutions of the Euler equations. © 2022, CC BY.

关键词： Shear flow

Machine learning from a continuous viewpoint,I

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Science China mathematics 2020年第11期63卷 2233-2266页

作者： Weinan E Chao Ma Lei Wu Department of Mathematics Princeton UniversityPrincetonNJ 08544USA The Program in Applied and Computational Mathematics Princeton UniversityPrincetonNJ 08544USA Beijing Institute of Big Data Research Beijing 100871China

We present a continuous formulation of machine learning,as a problem in the calculus of variations and differential-integral equations,in the spirit of classical numerical *** demonstrate that conventional machine learning models and algorithms,such as the random feature model,the two-layer neural network model and the residual neural network model,can all be recovered(in a scaled form)as particular discretizations of different continuous *** also present examples of new models,such as the flow-based random feature model,and new algorithms,such as the smoothed particle method and spectral method,that arise naturally from this continuous *** discuss how the issues of generalization error and implicit regularization can be studied under this framework.

关键词： machine learning continuous formulation flow-based model gradient flow particle approximation

INVARIANTS FOR NEURAL AUTOMATA

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arXiv 2023年

作者： Uria-Albizuri, Jone Carmantini, Giovanni Sirio Graben, Peter Beim Rodrigues, Serafim University of the Basque Country Department of Mathematics Leioa Spain foldAI Munich Germany Bernstein Center for Computational Neuroscience Berlin Germany Basque Center for Applied Mathematics Bilbao Spain

computational modeling of neurodynamical systems often deploys neural networks and symbolic dynamics. One particular way for combining these approaches within a framework called vector symbolic architectures leads to neural automata. An interesting research direction we have pursued under this framework has been to consider mapping symbolic dynamics (e.g. performed by Turing machines) onto neurodynamics, represented as neural automata. This representation theory, enables us to ask questions, such as, how does the brain implement Turing computations. Specifically, in this representation theory, neural automata result from the assignment of symbols and symbol strings to numbers, known as Gödel encoding. Under this assignment symbolic computation becomes represented by trajectories of state vectors in a real phase space, that allows for statistical correlation analyses with real-world measurements and experimental data. However, these assignments are usually completely arbitrary. Hence, it makes sense to address the problem question of, which aspects of the dynamics observed under such a representation is intrinsic to the dynamics and which are not. In this study, we develop a formally rigorous mathematical framework for the investigation of symmetries and invariants of neural automata under different encodings. As a central concept we define patterns of equality for such systems. We consider different macroscopic observables, such as the mean activation level of the neural network, and ask for their invariance properties. Our main result shows that only step functions that are defined over those patterns of equality are invariant under symbolic recodings, while the mean activation, e.g., is not. Our work could be of substantial importance for related regression studies of real-world measurements with neurosymbolic processors for avoiding confounding results that are dependant on a particular encoding and not intrinsic to the dynamics. Copyright © 2023, The Authors. Al

关键词： Dynamics

Two-plasmon-decay instability stimulated by dual laser beams in inertial confinement fusion

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Matter and Radiation at Extremes 2025年第1期10卷 48-56页

作者： C.-W.Lian Y.Ji R.Yan J.Li L.-F.Wang Y.-K.Ding J.Zheng Department of Modern Mechanics University of Science and Technology of ChinaHefeiAnhui 230026China Collaborative Innovation Center of IFSA Shanghai Jiao Tong UniversityShanghai 200240China Department of Plasma Physics and Fusion Engineering University of Science and Technology of ChinaHefei 230026China Institute of Applied Physics and Computational Mathematics Beijing 100088China

Two-plasmon-decay instability(TPD)poses a critical target preheating risk in direct-drive inertial confinement *** this paper,TPD collectively driven by dual laser beams consisting of a normal-incidence laser beam(Beam-N)and a large-angle-incidence laser beam(Beam-L)is investigated via particle-in-cell *** is found that significant TPD growth can develop in this regime at previously unexpected low laser intensities if the intensity of Beam-L exceeds the large-angle-incidence *** beams contribute to the growth of TPD in a“seed-amplification”manner in which the absolute instability driven by Beam-L provides the seeds that are convectively amplified by Beam-N,making TPD energetically important and causing significant pump depletion and hot-electron generation.

关键词： laser pump decay

Atomic determination of the nuclear quadrupole moment Q(209Bi) using the multi-configuration Dirac-Hartree-Fock method

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arXiv 2025年

作者： Li, Jiguang Bieron, Jacek Godefroid, Michel Jönsson, Per Institute of Applied Physics and Computational Mathematics Beijing100088 China Instytut Fizyki Teoretycznej Uniwersytet Jagielloński Kraków Poland Université Libre de Bruxelles Brussels1050 Belgium Department of Materials Science and Applied Mathematics Malmö University MalmöS-20506 Sweden

The multiconfiguration Dirac-Hartree-Fock method implemented in the Grasp2018 package was employed to calculate the magnetic dipole hyperfine interaction constants and electric field gradients of levels in the ground configuration of the neutral bismuth atom. Combining the calculated electric field gradient of the ground state with the measured electric quadrupole hyperfine interaction constant, we extracted the nuclear quadrupole moment for the 209Bi isotope, Q(209Bi) = −422(22) mb. This value, together with other results obtained from atomic- and molecular-structure calculations, created the "world average" nuclear quadrupole moment of this isotope, Q(209Bi) = −420(17) mb. © 2025, CC BY.

关键词： Atoms